Robust decision making and convex risk measures computation

Abstract

The main aim of the present thesis is to investigate the effect of diverging priors concerning modeluncertainty on decision making. One of the main issues in the thesis is to assess the effect of differentnotions of distance in the space of probability measures and their use as loss functionals in theprocess of identifying the best suited model among a set of plausible priors. Another issue, is thatof addressing the problem of \inhomogeneous" sets of priors, i.e. sets of priors that highly divergentopinions may occur, and the need to robustly treat that case. As high degrees of inhomogeneity maylead to distrust of the decision maker to the priors it may be desirable to adopt a particular prior correspondingto the set which somehow minimizes the \variability" among the models on the set. Thisleads to the notion of Frechet risk measure. Finally, an important problem is the actual calculationof robust risk measures. An account of their variational definition, the problem of calculation leadsto the numerical treatment of problems of the calculus of variations for which reliable and effectivealgorithms are proposed. The contributions of the thesis are presented in the following three chapters.